Poisson
Calculator

Clearly, the Poisson formula requires many time-consuming computations. The Stat
Trek Poisson Calculator can do this work for you - quickly, easily, and
error-free. Use the Poisson Calculator to compute Poisson probabilities and
cumulative Poisson probabilities. The
calculator is free. It can be found under the Stat Tables
tab, which appears in the header of every Stat Trek web page.

Cumulative Poisson Probability

A cumulative Poisson probability refers to the probability that
the Poisson random variable is greater than some specified lower limit
and less than some specified upper limit.

Example 1

Suppose the average number of lions seen on a 1-day safari is 5. What is the
probability that tourists will see fewer than four lions on the next 1-day
safari?

Solution: This is a Poisson experiment in which we know the following:

μ = 5; since 5 lions are seen per safari, on average.

x = 0, 1, 2, or 3; since we want to find the likelihood that tourists will see
fewer than 4 lions; that is, we want the probability that they will see 0, 1,
2, or 3 lions.

e = 2.71828; since e is a constant equal to approximately 2.71828.

To solve this problem, we need to find the probability that tourists will see 0,
1, 2, or 3 lions. Thus, we need to calculate the sum of four probabilities:
P(0; 5) + P(1; 5) + P(2; 5) + P(3; 5). To compute this sum, we use the Poisson
formula: